Classification of some cosets of the Reed-Muller code

This paper presents a descending method to classify Boolean functions in 7 variables under the action of affine general linear group. The classification determines number classes, set orbits representatives and generator stabilizer each representative. consists iteration process $$RM(k, m)/RM(r-1, m)$$ from that RM(k, m)/RM(r, m). We namely obtain classifications RM(4, 7)/RM(2, 7) RM(7, 7)/RM(3, 7), which we deduce some consequences on covering radius RM(3, near bent functions.